Question

3. A part- When asked, "Do kids regularly carry weapons in your school?" 14,254 students said yes, and 115,334 students said no. With a 95% level of confidence, find the margin of error (MOE) associated with the sample proportions. (Give the answer to one decimal place, if needed.)
MOE = ____%

B part- A poll pertaining to environmental concerns had the following footnote: "Based on a sample of 1,768 adults, the margin of error is plus or minus 2.3percentage points." Find the level of confidence (α) of the poll. (Give the answer to three decimal places, if needed.)
α =____

C part- Find the z-number associated with a 73% level of confidence. (Round the answer to two decimal places.)
z = ____

Answer 1

3)

Solution :

Given that,

n = 115334

x = 14254

Point estimate = sample proportion = = x / n = 14254 / 115334 = 0.124

1 - = 1 - 0.124 = 0.876

  At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.124 * 0.876) / 115334.124-)

= 0.002

MOE = 0.2%

C)

At 73% confidence level the z is ,

= 1 - 73% = 1 - 0.73 = 0.27

/ 2 = 0.27 / 2 = 0.135

Z_/2 = Z_0.135 = 1.10

z = 1.10